Efficient Inverse Modeling of Perceptual Sound Matching with Differentiable Synthesizers

Core Concepts

The core message of this article is to propose a novel "perceptual-neural-physical" (PNP) loss function that can efficiently optimize a neural network to retrieve the input parameters of a differentiable synthesizer in order to best imitate a target audio signal, while preserving perceptual fidelity.

Abstract

This article addresses the problem of designing a suitable loss function for perceptual sound matching (PSM) when the training set is generated by a differentiable synthesizer. The main contribution is the PNP loss, which aims to address the tradeoff between perceptual relevance and computational efficiency. The key idea behind PNP is to linearize the effect of synthesis parameters upon auditory features in the vicinity of each training sample. This linearization procedure is massively parallelizable, can be precomputed, and offers a 100-fold speedup during gradient descent compared to differentiable digital signal processing (DDSP). The authors demonstrate PNP on two datasets of nonstationary sounds: an AM/FM arpeggiator and a physical model of rectangular membranes. They show that PNP is able to accelerate DDSP with joint time-frequency scattering transform (JTFS) as auditory feature, while preserving its perceptual fidelity. Additionally, the authors evaluate the impact of other design choices in PSM: parameter rescaling, pretraining, auditory representation, and gradient clipping. They report state-of-the-art results on both datasets and find that PNP-accelerated JTFS has greater influence on PSM performance than any other design choice.

Stats

The AM/FM arpeggiator dataset has 27,000 samples with parameters sampled from the intervals: fc ∈ [512, 1024] Hz, fm ∈ [4, 16] Hz and γ ∈ [0.5, 4] Hz. The drum sound synthesizer dataset has 100,000 samples with parameters sampled from the intervals: log ω0 ∈ [40, 1000] Hz, τ0 ∈ [0.4, 3] s, log p ∈ [-5, -0.7], log D ∈ [-5, -0.5], and α ∈ [0.0001, 1].

Quotes

"PNP is the optimal quadratic approximation of a given L2 perceptual loss. It adopts a bilinear form whose kernel matrix is the Riemannian metric formed by the differentiable map (Φ ◦ g)." "We propose a corrective term added onto the kernel matrix, as a mechanism to reduce the condition number of the kernel matrix in case where the inverse problem is ill-conditioned."

Key Insights Distilled From

Learning to Solve Inverse Problems for Perceptual Sound Matching

by Han Han,Vinc... at arxiv.org 05-07-2024

https://arxiv.org/pdf/2311.14213.pdf

Deeper Inquiries

How can the proposed PNP loss be extended to handle more complex synthesizers with discrete elements, thresholding or nonlinear analog effects

The proposed PNP loss can be extended to handle more complex synthesizers with discrete elements, thresholding, or nonlinear analog effects by incorporating additional layers or modules in the neural network architecture. Discrete Elements: For synthesizers with discrete elements, the PNP loss can be adapted to include specific functions or operations that account for the discrete nature of the elements. This could involve creating a mapping function that translates the discrete elements into a continuous space for better optimization. Thresholding: To handle thresholding effects in synthesizers, the PNP loss can be modified to include thresholding functions or constraints in the loss calculation. By incorporating the thresholding behavior into the loss function, the neural network can learn to optimize parameters while considering the thresholding effects. Nonlinear Analog Effects: For synthesizers with nonlinear analog effects, the PNP loss can be enhanced by introducing nonlinear activation functions or layers in the neural network. These nonlinear components can capture the complex analog effects and ensure that the optimization process accounts for these nonlinearities. By customizing the neural network architecture and loss function to accommodate the specific characteristics of complex synthesizers, the PNP loss can be extended to effectively handle a wider range of synthesizer types with diverse elements and effects.

What are the potential limitations of the PNP loss approach, and how could it be further improved to handle a wider range of perceptual sound matching tasks

The potential limitations of the PNP loss approach include: Complexity of Synthesizers: The PNP loss may struggle with highly complex synthesizers that involve intricate interactions between parameters and perceptual features. In such cases, the linearization assumptions of the PNP loss may not hold, leading to suboptimal results. Ill-Conditioned Problems: In scenarios where the inverse problem is ill-conditioned, the PNP loss may face challenges in providing stable and reliable solutions. The regularization techniques used in the loss function may need further refinement to handle ill-conditioned problems effectively. Limited Generalization: The PNP loss approach may have limitations in generalizing to a wide range of perceptual sound matching tasks beyond the specific datasets and synthesizers it was trained on. Enhancements in the model's ability to adapt to diverse sound characteristics could improve its generalization capabilities. To further improve the PNP loss approach, the following strategies can be considered: Enhanced Regularization: Implement more sophisticated regularization techniques to address ill-conditioned problems and improve the stability of the optimization process. Adaptive Learning: Incorporate adaptive learning rate strategies to dynamically adjust the learning rate based on the loss landscape, ensuring efficient convergence and avoiding oscillations. Data Augmentation: Introduce data augmentation techniques to diversify the training data and enhance the model's ability to generalize to unseen synthesizers and sound variations. By addressing these limitations and implementing these improvements, the PNP loss approach can be enhanced to handle a wider range of perceptual sound matching tasks effectively.

Given the success of the JTFS representation, how could the proposed framework be adapted to leverage other perceptual audio features or representations that capture different aspects of sound perception

Given the success of the JTFS representation, the proposed framework can be adapted to leverage other perceptual audio features or representations by following these steps: Feature Selection: Identify alternative perceptual audio features or representations that capture different aspects of sound perception, such as pitch, timbre, or rhythm. These features should be relevant to the specific sound matching task at hand. Model Modification: Modify the neural network architecture to accommodate the new audio features or representations. This may involve adding additional layers or modules to process and extract information from the chosen features effectively. Loss Function Integration: Update the loss function to incorporate the new perceptual audio features or representations. Ensure that the loss function aligns with the chosen features and accurately measures the perceptual distance between the target sound and the synthesized sound. Training and Evaluation: Train the model using the adapted framework with the new audio features and evaluate its performance on the sound matching task. Compare the results with the JTFS-based approach to assess the effectiveness of the new features. By adapting the framework to leverage different perceptual audio features or representations, the model can be tailored to specific sound matching tasks and potentially achieve improved performance and accuracy.